Is there a way to save strokes while painting/sculpting?
What you would be trying to record really would be the effect of the movements (sculpting) rather than the actions themselves. Because, the actions themselves have context. The movements of a pen or mouse device make sense only when in "Edit" or "Sculpt" mode.

Now, theoretically, you could respond to a set of events from the user interface and keyframe the effects of those actions to be able to "record" and "play back". But the amount of information and frequency required to do this probably would make the whole thing unusable but for small scale projects. (And in any case, you would still be key-framing the changes applied to the object by the actions, rather than the actions themselves).

But, if we are talking about keyframing mesh modifications, then Blender does already have something that could be of help in this case. It is called "Shape Keys".

Shape keys store intermediate states of a model's mesh and also allow for interpolation between these intermediate states.

The workflow to achieve this "recording" might seem a bit awkward but would consist of mainly two steps: 1) Add a shape key 2) Apply the sculpting "brush stroke".

In the end, you will have a set of shape keys that show the progressive deformation of the mesh, potentially, brush stroke by brush stroke.

You can now key frame the transitions between shape keys to affect the dynamics of the deformations and create an animation that is as fast or as slow as you like.

This would look more like morphing, of course, rather than sculpting, except in the case where you could subdivide one stroke to many different stages.

One thing that could be done to improve the presentation of the effect would be to have the mesh rotating in front of a static camera and apply the transitions when the affected side of the mesh goes off the view. It would give the apperance of more details added with each revolution without the viewer actually seeing the deformations take place.